alternative use of 6- or 26-adjacency corresponds to open or closed sets in the 3D grid cell topology. Grid cell topology also applies to multilevel (e.g., color) 2D or 3D images, for example based on a total order of possible image values and applying a 'maximum-label rule' (see the book by Klette and Rosenfeld, 2004). Digital topology is highly related to combinatorial topology. The main differences between them are: (1) digital topology mainly studies digital objects that are formed by grid cells, and (2) digital topology also deals with non-Jordan manifolds. A combinatorial manifold is a kind of manifold which is a discretization of a manifold. It usually means a piecewise linear manifold made by simplicial complexes. A digital manifold is a special kind of combinatorial manifold which is defined in digital space i.e. grid cell space. A digital form of the Gauss–Bonnet theorem is: Let M be a closed digital 2D manifold in direct adjacency (i.e., a (6,26)-surface in 3D). The formula for genus is , where indicates the set of surface-points each of which has i adjacent points on the surface (Chen and Rong, ICPR 2008). If M is simply connected, i.e., , then . (See also Euler characteristic.) See also Digital geometry Combinatorial topology Computational geometry Computational topology Topological data analysis Topology Discrete mathematics Geospatial topology References Vladimir A. Kovalevsky. (2008).